Historically, the main efforts in solving the problem of ghosts was
related to the quantum aspects. In this respect we can start the
list from the mentioned paper by Veltman [1]},
regardless it has nothing specific about quantum gravity. Soon
after the seminal work of Stelle [2]} with the proof of
renormalizability of the fourth-derivative QG, there were first
works about solving the problem of ghosts [3]} and
[4]}. The main common idea of these works was that the loop
corrections to the propagator (REF ) transform the unique
massive pole into a pair of the complex conjugate poles, with the
positions of these poles being gauge fixing dependent [5]}.
In this case, one can
prove the unitarity of the \(S\) -matrix, violated by the presence of
massive ghosts [2]}. Unfortunately, it was shown
[7]}, that definite conclusion on this issue can be taken
only on the basis of exact knowledge of the dressed
propagator of \(h_{\mu \nu }\) . E.g., the one-loop corrections or
the \(1/N\)  approximation are insufficient for solving the problem.
It is interesting that starting from the six-derivative theory, one
can provide the desirable features (pair of complex conjugate
poles, for instance) already at the tree-level and, also, prove that
the loop corrections do not change this structure. In this
situation, one can use the optical theorem and prove the unitarity
of the \(S\) -matrix in the Lee-Wick approach [8]}.
